JP11-303621A issued in 1999 by the Japan Patent office relates to accurate detection of deterioration of a NOx trap catalyst arranged downstream of a three-way catalyst independently of a deteriorated state of the three-way catalyst. Specifically, the deteriorated state of the three-way catalyst is determined based on an output inversion time of an O2 sensor downstream of the NOx trap catalyst in a stoichiometric operation. In this prior art is disclosed, as a stoichiometric control, an air-fuel ratio feedback control of skipping a proportional term as a feedback correction coefficient when the output of the O2 sensor at the downstream side is switched from rich to lean and, thereafter, adding integral terms until the output is switched to rich. Here, since a switching time of the O2 sensor from rich to lean or from lean to rich is proportional to oxygen storage capacity of the three-way catalyst, deterioration of the three-way catalyst is detected based on the inversion time of the output of the O2 sensor.
Then, after an air-fuel ratio is maintained at a lean side and oxygen and NOx are respectively maximally adsorbed by the three-way catalyst and the NOx trap catalyst, an exhaust gas air-fuel ratio is changed to a rich side. Based on the output of the O2 sensor arranged downstream of the NOx trap catalyst at this time, oxygen storage capacity and NOx adsorption capacity of the three-way catalyst and the NOx trap catalyst are detected from a time during which an air excess ratio λ remains near a stoichiometric air-fuel ratio. If the above detection on deterioration of the three-way catalyst is considered, deterioration of the NOx trap catalyst can be specified.